A test of the dependence of an optimal control field on the number of molecular degrees of freedom: HCN isomerization

Abstract

This paper reports the results of a study of the robustness of the field required to generate the isomerization reaction HCN→CNH as a function of number of degrees of freedom and the complexity of the description of the dynamics. The particular reduced state representation of the control process that is tested in this paper is the reaction path method proposed by Zhao and Rice. We show that if the description of the system dynamics includes vibrational motions perpendicular to the one-dimensional reaction path and both the interactions between those vibrations and between them and the reaction path, the fields found by the conventional computational scheme represent local optima, and none of these correspond to generating a transfer of 100% of the population from the ground vibrational state of HCN to a mixture of vibrational states of CNH. Moreover, it is very difficult to find fields that will efficiently transfer population from the ground vibrational state of HCN to particular vibrational states of CNH. Comparing the optimized control fields reported in this paper with those previously obtained using simplified versions of the reaction path reduction, one finds that the complexity ͑measured by the power spectra͒ of optimal control fields increases as the dynamical description includes more degrees of freedom and then the interactions between all of the degrees of freedom. The optimal control field generated using a simpler dynamical description is not a good guide to the optimal control field associated with a more complex dynamical description. We conclude that the reaction path method of reduction of the complexity of calculation of the optimal field required to drive a particular reaction is not likely to be useful for the design of fields with which to actively control reactions of polyatomic molecules.

Phase space conduits for reaction in multidimensional systems: HCN isomerization in three dimensions

“…Moreover, as we make clear below, these spherical cylinders bound the true ''phase space reaction paths.'' The ability to compute these manifolds, and to track them far away from the transition region, is the key to the study of state-specific reactivity, 16,17 of dynamical effects on reactions 30,31 of control of reactivity 18,19 and as will be discussed below in more detail, of rare events.…”

Optimal control of a Cope rearrangement by coupling the reaction path to a dissipative bath or a second active mode

“…The relevance of a reduced space simulation in a molecular control has already been addressed in the case of the HCN isomerization. 57 As expected, replacing the one-dimensional (1D) reaction path by a two-dimensional (2D) model dramatically increases the state density, particularly in the case of a Cope rearrangement which is characterized by a very wide and flat transition region. Therefore, the pulses obtained in the previous work 54 are too short to control the process.…”

Laser control of proton motion in porphyrin derivative

“…Because of the robustness of the laser parameters, we employed STIRAP to control the proton motion of 1-methylmalonaldehyde [22][23][24] and determined the effective pulse sequence to yield the complete proton transfer, by applying STIRAP to the one-dimensional asymmetric double-well potential. Rice and coworkers [25,26] also applied STIRAP to the control of the geometrical isomerization reaction of the HCN-CNH system. Several generalizations of STIRAP [27][28][29] have been proposed, including several intermediate states for N-level systems.…”